Rotations

GeometryUnit 7, Lesson 3Mrs. King

What is a Rotation?

Definition:

A turn. Example?

London Eye

Directions of Rotations!

Positive rotations go in a counterclockwise direction.

Negative rotations go in a clockwise direction.

Clockwise

                Counterclockwise

                

Illustration from: http://www.regentsprep.org/Regents/math/geometry/GT4/Lrotate.htm

Rotation Rule

90°: (x,y)(-y,x)

Swap the numbers and change the new “x” value sign.

Rotation Rule

90°:

180°:

270°:

360°:

(x,y)(-y,x)

Rotate 90° two times

Rotate 90° three times

NOTHING!

Graphing Coordinates

Rotate the point (4,7):– 90°:

– 180°:

– 270°:

– 360°:

y

x

10

10

-10

-10

(-7,4)

(-4,-7)

(7,-4)

(4,7)

(4,7)

(-7,4)

(-4,-7)

(7,-4)

Example 1:

Graph the vertices of parallelogram WXYZ.– W(-7,1)– X(-3,1)– Y(-2,5)– Z(-6,5)

Rotate the parallelogram 90°.

y

x

10

10

-10

-10

W X

YZW’(-1,-7)X’(-1,-3)Y’(-5,-2)

Z’(-5,-6)W’

X’Y'

Z’

Example 2:

Graph the vertices of parallelogram WXYZ.– W(-7,1)– X(-3,1)– Y(-2,5)– Z(-6,5)

Rotate the parallelogram 270°.

y

x

10

10

-10

-10

W X

YZW’(1,7)X’(1,3)Y’(5,2)

Z’(5,6)

W’

X’Y'

Z’(-1,-7) (7,-1)

Practice with Rotations

http://www.regentsprep.org/Regents/math/geometry/GT4/PracRot.htm

Practice:

A(2,3), B(2,-1), C(-1,-1) Graph triangle ABC under the following rotations:

Answer: